Problem: Solve for $x$ and $y$ using elimination. ${-2x+3y = 23}$ ${5x-5y = -35}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${-10x+15y = 115}$ $15x-15y = -105$ Add the top and bottom equations together. $5x = 10$ $\dfrac{5x}{{5}} = \dfrac{10}{{5}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-2x+3y = 23}\thinspace$ to find $y$ ${-2}{(2)}{ + 3y = 23}$ $-4+3y = 23$ $-4{+4} + 3y = 23{+4}$ $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {5x-5y = -35}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ - 5y = -35}$ ${y = 9}$